Exact and approximate results for convex envelopes of special structured functions over simplices

In this paper we describe how to derive the convex envelope of a function f over the n-dimensional unit simplex \(\Delta _n\) at different levels of detail, depending on the properties of function f, by starting from its definition as the supremum of all the affine underestimators of f over \(\Delta _n\). At the first level we are able to derive the closed-form formula of the convex envelope. At the second level we are able to derive the exact...